Fading out of particles
This is easy to do in the material of your particle object. heres a picture of my node setup 

If you want a tutorial showing how i made this, Blender Guru has a tutorial on making sparks. 

hope this helps

EDIT: you can adjust the color ramp, to adjust how soon the particles fade out and how long it takes.

Here's how it works:

the particle info node takes into account the particle settings.  It then allows you to access them in the material with it's output connections.  In this example, I divided the age by the lifetime, which gives me a the age of the particle, but also takes into account how long the particle will live, so we can use that value to effect the material.  The color ramp provides the control you need to adjust how soon it fades out and how it does.  you could use this for even more complex effects, like repeated flashing if you wanted to.  the value on the left of the color ramp is the start of the particles life, while the value on the right of the color ramp is the end.  Using this as the factor between an emission node and a transparent, causes it to fade around the middle of it's lifetime, (due to the way my color ramp is set up).  

you can use the same principle to change the color of the particle over lifetime, the strength of the emission over lifetime, and almost anything else.  I hope this edit has been useful, and that you can use it for more blends.